Tuesday, July 13, 2010

Idiot Proofing Thermodynamics


Many thanks to Graciel Ilar for commenting on my post here and kindly providing the “open system” argument (with actual numbers plugged in - see below) showing that evolution doesn’t violate the second law of thermodynamics.

Although this argument is, in my opinion, valid it is not sufficiently idiot proof to convince those who are too intuitively compelled by the apparent antithesis between the rubric “increasing disorder” and evolution. For example, Granville Sewell of Uncommon Descent affiliation is not convinced by the open system argument.

For non-technical readers, the gist of the open system argument is actually easy to understand: It observes that the reduction in entropy required by life is extremely large. But the Earth is an open system that receives useable heat from the Sun implying a concomitant increase in entropy as the Sun uses up its store of free energy. Thus the increase in entropy of the Sun-Earth system as the Sun transfers heat to the Earth by far and away overwhelms the relatively small decrease in entropy required by life, thus restoring an overall increase in entropy. The weakness of 2LoT as a measure of what is going on is that it only tells us what is happening in the total “bank account” and not the sub accounts: There may be an overall loss in cash, any yet some accounts could still be increasing, but not fast enough to compensate for the general downturn in fortune.

Anti-evolutionists do not understand this argument because they just cannot see where the information is coming from to configure those ordered yet complex life forms. For them there is a strongly sensed intuitive contradiction between the compelling rubric “increasing disorder” and the localized increases in complex order we see with evolution. They have no trouble with crystal formation because they can see that the information here is coming from the laws of physics in a fairly straight forward and accountable way, but they just can’t see how the laws of physics do this for the “crystallization” of living structures.

The reason why anti-evolutionists often stumble on the entropy argument is that they don’t really understand what entropy measures. Entropy is given by S = k Log Z where k is Boltzmann’s constant and Z is the number of microstates consistent with a macro state. In the word “consistent” is embodied all that the laws of physics allow, or rather don’t allow: For the laws of physics themselves are not subject to entropy increases and they eliminate huge numbers of possible universes; thus, with respect to all that is possible our universe is highly ordered even at its most disordered. Therefore a system can move toward maximum disorder and yet remain highly ordered in an absolute sense.

However, what I would concede is that even though 2LoT is too loose a mathematical statement to contradict evolution in and of itself this doesn’t mean that evolution has actually occurred; it is conceivable that the laws of physics simply don’t eliminate enough paths through phase space to make evolution even remotely probable. Hence a measure of open mindedness is required. But I’m not open minded because people like Granville Sewell fail to understand thermodynamics and present superficial arguments against evolution; he’s going to have to think a lot harder if he is going to bring down evolution. Sewell often asks the rhetorical question “Can anything happen in an Open System?” expecting the answer “no” to be the answer unfavourable to evolution. But the irony is that if evolution has occurred it would be precisely because physics prevents anything happening in an open system that evolution is favoured!

****


Mr T Reeves thank you for an insightful article. It has been proven beyond reasonable doubt that Evolution does *not* violate the 2LOT. Excerpt from the article:

When heat is transferred from one object to another, there is a change in entropy associated with that transfer:

dS = Q/T

where dS is the change in entropy, Q is the quantity of heat transferred, and T is the temperature of the object.

The earth is being bathed in radiation by the sun: the sun is giving off energy, some of which is received by the earth.

The rate of energy transfer is known:

P = dQ/dt = 1.2 x 10^17 W

when you sum over the whole surface of the earth; this is how much energy the earth receives from the sun per second (i.e. a lot).

Thus we can calculate the rate of entropy production of the earth/sun system:

dS/dt = P/Te - P/Ts

where Ts is the temperature of the sun, and Te is the temperature of the earth.

Since the sun is ~20x hotter than the earth, the P/Te term is ~20x larger than the P/Ts term.

Thus

dS/dt ~ P/Te

and plugging in numerical values, P ~ 1.2 x 10^17 W and Te = 300K,

dS/dt ~ 4 x 10^14 J/K/second

The gist: dS/dt is positive, and it's HUGE - the entropy of the sun-earth system is extremely rapidly increasing with time!

(Note that this does not include the eventuality that this radiation will (though on extremely long timescales) thermalize in deep space with the 3K CMB, which results in a further increase in entropy about 100 times larger!)

Now, how much of an entropy *decrease* is associated with the evolution of life? If it's greater than the above, there is a problem. But if it's less than the above, then the second law is satisfied, in that

deltaS_total = deltaS_sun + deltaS_life > 0

This can't be done as rigorously, but estimates can be made.

However, from thermodynamics we have the result

mu/T = -dS/dN

which, rearranged, gives us

deltaS = -N*mu/T

where mu is the chemical potential for a molecule and N is the number of molecules on the earth's surface.

The reduction in entropy due to the formation of life on earth (which we may consider as an ordering of all the molecules forming the earth's biomass), relative to that of a barren earth, is thus:

deltaS_life = S_earth_with_life - S_dead_earth ~ -Nb*mu/T

where Nb is the total number of molecules in the earth's biomass.

For a typical ideal gas, mu ~ 10*kb*T where kb is Boltzmann's constant.

The total biomass of earth is Nb ~ 10^41 (about 10^15 kg). Even multiplying by a factor of 100 to account for nonliving matter that might nevertheless be crucial to the evolution of life, Nb ~ 10^43.

Plugging the numbers in (including the factor of 100), we find that

|deltaS_life| ~ 10^44 * kb

This is a HUGE value, which leads to the mistaken impression that evolution violates the second law of thermodynamics.

However, let's compare that to the earlier value we found for the rate of increase in entropy due to the sun's radiation:

dS/dt_sun = 4 x 10^14 J/K/s = 3 x 10^37 kb/s

Dividing the two by each other

deltaS_life / dS/dt_sun = 3 x 10^6 seconds = minimum time allowable for evolution of life

3 x 10^6 seconds is about a month.

Conclusion: As long as the evolution of life on earth took more than about a month, it does not violate the second law of thermodynamics.

Even YECs agree that the earth is more than one month old.

Note that this does *not* imply that the evolution of life took a month; this is a highly idealized situation and only derives a lower limit on the time using basic physics.

The actual evolution of life took much longer, by a factor of billions.

But just one month of insolation adds enough entropy to the earth to offset the entropy decrease required to form all of the biomass on earth.

Even if this were an underestimate by a factor of a thousand, then only one hundred years would have been required to offset the reduction in entropy caused by the evolution of life.


2 Comments:

Anonymous Physics Major said...

2nd LoT has many forms. Can you make the same defense of Evolution using the Statistical Mechanics form of the 2nd law?

10:00 PM, November 11, 2013  
Blogger Timothy V Reeves said...

That's exactly the point. Read what I have written:

However, what I would concede is that even though 2LoT is too loose a mathematical statement to contradict evolution in and of itself this doesn’t mean that evolution has actually occurred; it is conceivable that the laws of physics simply don’t eliminate enough paths through phase space to make evolution even remotely probable

My instinctual gut reaction is that physics is unlikely to provide sufficiently constrained probabilistic envelopes to make the thermodynamic searching of standard evolution likely. (I probably have a lot in common will William Dembski in this respect.)

But let me stress that I recognise a gut when I have one - it's not proof. It may well be that ultimate proof is hamstrung by the computational irreducibility of the problem in hand.

My guess that you are have identified yourself with one of the polarised partisan groups where the passions clouds wits and nuanced augments are drowned by the shouting.

5:48 AM, November 12, 2013  

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